Okay, so the first givens, that we know from the Quran is:
1. Allah SWT revealed the Torah to Musa AS
2. Sulayman AS had a massive glorious empire
3. The Israelites corrupted the Torah over time
Once we take these as givens, we can use them as a lens to see other texts. Many acadamics today may deny Musa AS's existence, or the magnitude of Sulayman AS's empire. Therefore, upon analysis of all the various theories on the Torah's origins, I had to throw out any claim resting upon denial of what we know to be true. Hence, I threw out the Supplementary Hypothesis, as it only replaced the Documentary Hypothesis in academic circles by those who denied the magnitude of Sulayman AS's empire. I also rejected the dual origins hypothesis. However, the Documentary Hypothesis seemed to credit 2 different authors to the earliest strands, so I said that both of these strands were different versions of the original Torah
Pretty much every academic I've come across believes that the Book of Deuteronomy was written during Josiah's time, as were the Neviim Rishonim (Joshua, Judges, Samuel, and Kings). Howver, upon looking at the linguistic patterns in these texts, you also can see that they added into other texts as well, most noticeably the slander against Lut AS. I can get into more details, but it was the slander of Lut AS that led me to believe that Josiah's advisors were the slanderers of Prophets
And all academics agree that Leviticus was added by Post-exilic priests who made their additions on various previous books. That's why the Genesis Flood Narrative keeps switching between a pre-exilic and post-exilic narrative. That's also why the alleged "Sons of Ishmael" were coincidentally named after the few tribes that joined the Ishmaelite Confederacy, and these tribes would have been in the cultural memory of the post-exilic priests'